This paper presents a feedback receiver for the digital predistortion (DPD) of radio frequency (RF) power amplifiers (PAs). In contrast to conventional architectures, the receiver samples in the frequency domain. By randomly selecting a frequency bin in each sampling interval, the PA model is identified with substantially lower acquisition bandwidth and sampling rate. The receiver prototype is implemented in a 28-nm FD-SOI technology and samples at 4MS/s instead of the full Nyquist rate of 168MS/s for a 20-MHz Long Term Evolution (LTE) signal with spectral regrowth. The prototype is shown to linearize a 4-W small base station power amplifier from an adjacent channel leakage ratio (ACLR) of -35 dBc to -47.7 dBc, after processing only about 250 samples.